# Salp swarm algorithm-based model predictive controller for frequency regulation of solar integrated power system

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## Abstract

Global analysis of power system markets project frequency regulation as one of the most profitable ancillary services. It is associated with second-to-second balance of load and frequency within a control area and acquires a principal role in enabling power interchanges while offering better conditions for electricity exchange. In the light of the above, a novel control strategy, namely salp swarm algorithm (SSA)-based model predictive controller, is proposed for frequency regulation of an unequal two-area realistic power system, incorporating solar thermal power plant and conventional thermal plant. Governor dead band, generation rate constraint and transport delay are considered in each control area. Over the past few years, model predictive controller (MPC) has come forward as a prediction-based control strategy for stabilizing dynamical systems while considering non-linearities, system uncertainties and constraints. The MPC parameters are optimized using SSA. The performance of the proposed approach is validated by comparing the dynamic time responses of SSA-optimized MPC with the other SSA-optimized conventional controllers, namely PID, FOPID and cascade PIDN-FOPID controller. The simulation result analysis shows that the proposed optimal MPC outpaces the conventional controllers with respect to peak overshoot, undershoot and settling time of the time responses. A comparative study of various objective functions indicates that, as compared to other indices, integral square error is better for the considered test system. Further, sensitivity analysis reveals the robustiousness of MPC parameters obtained at nominal values and hence is not required to be retuned, against variations in system loading and inertia constant.

## Keywords

Load frequency control (LFC) Salp swarm algorithm (SSA) Solar thermal power plant (STPP) Model predictive controller (MPC) Fractional-order proportional integral derivative (FOPID) Integral square error (ISE)## List of symbols

- \( f \)
Considered system frequency (Hz)

- \( i \)
Referred subscript to area

*i*, \( i \) = 1, 2- \( T_{12} \)
Synchronizing coefficient

- \( \Delta P_{Di} \)
Load variation in area \( i \) (p.u.)

- \( T \)
Simulation time (s)

- \( \Delta f_{i} \)
Frequency change in

*i*th area (Hz)- \( D_{i} \)
Δ

*P*_{Di}*/*Δ*f*_{i}(p.u. MW/Hz)- \( K_{si} \)
Gain of solar field of

*i*th area- \( B_{i} \)
Frequency bias constant of

*i*th area- \( \pi \)
pi

- \( K_{pi} \)
1

*/D*_{i}(Hz/p.u. MW)- \( H_{i} \)
Inertia constant of area \( i \) (s)

- \( \beta_{i} \)
(

*D*_{i}*+*1*/R*_{i}); area frequency response characteristics of*i*th area- \( R_{i} \)
Speed regulation parameter of governor of

*i*th area (Hz/p.u. MW)- \( \Delta P_{\text{tie}} \)
Incremental tie-line power deviation amid area 1 and area 2

- \( T_{gi} \)
Time constant of steam governor for thermal power plant in

*i*th area- \( K_{pfi} \)
Proportional gain of FOPID part of PIDN-FOPID cascade controller for

*i*th area*, i*= 1, 2- \( \mu_{i} \)
Order of differentiator of cascade PIDN-FOPID controller in

*i*th area*, i*= 1, 2- \( T_{ti} \)
Time constant of steam turbine for thermal power plant in

*i*th area- \( T_{gsi} \)
Time constant of steam governor for STPP in

*i*th area- \( a_{12} \)
Area capacity ratio

*T*_{pi}*2H*_{ i }*/f/D*_{ i }*T*_{o}Working fluid outlet temperature of solar field (°C)

*T*_{i}Working fluid inlet temperature of solar field (°C)

*T*_{e}Environmental temperature (°C)

*I*Solar irradiance (W/m

^{2})*v*Pump flow rate (m

^{3}/s)*A*Surface area of the collector

*C*Heat capacity of the working fluid (J/K)

*η*_{0}Solar field collector efficiency

*U*_{L}Total heat loss coefficient (W/m

^{2}K)*T*_{ri}Reheat steam turbine time constant of

*i*th area (s)*K*_{ri}Reheat coefficient of steam turbine of

*i*th area*K*_{pri}PID, FOPID, PIDN-FOPID proportional gain for

*i*th area*, i*= 1, 2*K*_{ini}PID, FOPID, PIDN-FOPID integral gain for

*i*th area*, i*= 1, 2*K*_{dei}PID, FOPID, PIDN-FOPID derivative gain for

*i*th area*, i*= 1, 2*N*_{i}PIDN-FOPID derivative filter coefficient for

*i*th area*, i*= 1, 2*K*_{dfi}Derivative gain of FOPID part of PIDN-FOPID cascade controller for

*i*th area*, i*= 1, 2*K*_{ifi}Integral gain of FOPID part of PIDN-FOPID cascade controller for

*i*th area*, i*= 1, 2*λ*_{i}Order of integrator of cascade PIDN-FOPID controller in

*i*th area*, i*= 1, 2*T*_{si}Solar collector time constant of

*i*th area*T*_{tsi}Time constant of steam turbine for STPP in

*i*th area

## Notes

### Acknowledgements

This research work is sponsored by the Council of Scientific & Industrial Research, New Delhi, India, under the Research and Development Project Grant 22(0692)/15/EMR-II.

### Compliance with ethical standards

### Conflict of interest

The authors declare that they have no conflict of interest.

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